Soler finished the nearly 100-mile run from Val-d'Isre to Brianon in four hours, 14 minutes and 24 seconds to collect his first career stage victory. The Tour de France's ninth stage involved three major climbs, and it was during the last climb when Soler took the lead.
The course also included a downhill sprint to the finish, which saw several contenders draw close to Soler. But the Colombian was able to cross first, beating runner-up Alejandro Valverde by 38 seconds. Cadel Evans also was timed at 38 seconds off Soler's pace.
Rasmussen, who won Sunday's stage of the race to take the overall lead, finished sixth Tuesday. But that, and the falling back of some racers who were high in the overall standings before hitting the Alps, allowed the Danish rider to establish a lead of 2 minutes, 35 seconds over Valverde and 2:39 over Iban Mayo.
With the Alps behind the racers, the Tour de France's Stage 10 Wednesday has a 143-mile course from Tallard to Marseille.